Selectivity Stefan

Vessman J, Stefan RI, van Staden JF, Danzer K, Lindner W, Burns DT, Fajgelj A, Muller H (2001) IUPAC, Analytical Chemistry Division, Commission on General Aspects of Analytical Chemistry Selectivity in analytical chemistry (IUPAC recommendations 2001). Pure Appl Chem 73 1381... 

Since interaction phenomena due to simultaneous diffusion of several components play an important role, the Maxwell-Stefan theory has been selected to describe the mass transfer processes. The general form of the flux expressions can be represented by (Taylor and Krishna, 1993)... 

So far, the selectivity of these membranes was tested only with regard to solutions of salt in water. There are indications however, from various sources, like the work of Peter and Stefan (O, that these membranes may be valuable for other separations. 

The mass diffusive flux m, of Equation (3.2) generally depends on the operating conditions, such as reactant concentration, temperature and pressure and on the microstructure of material (porosity, tortuosity and pore size). Well established ways of describing the diffusion phenomenon in the SOFC electrodes are through either Fick s first law [21, 34. 48, 50, 51], or the Maxwell-Stefan equation [52-55], Some authors use more complex models, like for example the dusty-gas model [56] or other models derived from this [57, 58], A comparison between the three approaches is reported by Suwanwarangkul et al. [59], who concluded that the choice of the most appropriate model is very case-sensitive, and should be selected, according to the specific case under study. 

Krishna and Paschek [91] employed the Maxwell-Stefan description for mass transport of alkanes through silicalite membranes, but did not consider more complex (e.g., unsaturated or branched) hydrocarbons. Kapteijn et al. [92] and Bakker et al. [93] applied the Maxwell-Stefan model for hydrocarbon permeation through silicalite membranes. Flanders et al. [94] studied separation of C6 isomers by pervaporation through ZSM-5 membranes and found that separation was due to shape selectivity. 

The behavior of the Fick diffusion coefficient in nonideal systems may be complicated, while the Maxwell-Stefan diffusion coefficients behave quite well, and are always positive for binary systems. In nonideal binary systems, the Fick diffusivity varies with concentration. As seen in Figure 6.1, water-acetone and water-ethanol systems exhibit a minimum diffusivity at intermediate concentrations. Table 6.1 displays the dependency of binary diffusivity coefficients on concentration for selected alkenes in chloroform at 30°C and 1 atm. As the nonideality increases, mixture may split into two liquid phases at certain composition and temperature. 

Stefan, R.-I. Baiulescu, G.-E. Aboul-Enein, H.Y. Ion-selective membrane electrodes in pharmaceutical analysis. Crit. Rev. Anal. Chem. 1997, 27, 307-321. 

Kaczmarski et al. used a similar model for the calculation of the band profiles of the enantiomers of 1-indanol on a chiral phase in HPLC [29,57]. These authors ignored the external mass transfer and assumed that local equilibrium takes place for each component between the pore surface and the stagnant fluid phase in the macropores (infinite fast kinetics of adsorption-desorption). They also assumed that surface diffusion contribution is much faster than pore diffusion and neglected pore diffusion entirely. Instead of the single file Maxwell-Stefan diffusion, these authors used the generalized Maxwell-Stefan diffusion (see Chapter 5).The calculation (see below) requires first the selection of equations to calculate the surface molecular flux [29,57,58],... 

In any event, we hope it is now well understood that mass transfer in multicomponent systems is described better by the full set of Maxwell-Stefan or generalized Fick s law equations than by a pseudobinary method. A pseudobinary method cannot be capable of superior predictions of efficiency. For a simpler method to provide consistently better predictions of efficiency than a more rigorous method could mean that an inappropriate model of point or tray efficiency is being employed. In addition, uncertainties in the estimation of the necessary transport and thermodynamic properties could easily mask more subtle diffusional interaction effects in the estimation of multicomponent tray efficiencies. It should also be borne in mind that a pseudobinary approach to the prediction of efficiency requires the a priori selection of the pair of components that are representative of the... 

J. Vessman, R.I. Stefan, J.F. van Staden, K. Danzer, W. Lindner, D.T. Burns, A. Fajgelj, H. Muller, Selectivity in analytical chemistry (IUPAC recommendations 2001), Pure Appl. Chem. 73 (2001) 1381. 

Fig. 14 Separation of C2H6/CH4 mixtures by permeation through a silicalite membrane, a Flux b selectivity. Continuous lines show the predictions of the Maxwell-Stefan model (Eq. 44) based on single-component diffusivities (Dqa> F>ob) with Dab from the Vignes correlation (Eq. 46). Dotted lines show predictions from the simplified Habgood model in which mutual diffusion effects are ignored (Eq. 45). From van de Graaf et al. [53] with permission...

Pick s first law describes equimolar diffusion, in which all components of the system may diffuse independent from each other. During thermal separation processes, matter is transported through phase boundaries. If a phase boundary is selectively permeable to one component, only one-directional diffusion is possible (an especially important case for absorption, adsorption, and drying). For one-directional diffusion, Stefan s law gives... 

In Chapter 2, Frank Steiner, Stefan Lamotte, and Stavros Kromidas go in detail into optimization strategies for RP-HPLC and discuss, on the basis of selected examples, which parameters seem promising in which case. 

A simple postirradiation radiochemical procedure has recently been developed at the Jozef Stefan Institute in Slovenia for the selective removal of iron from iron minerals and iron-based reference materials (Makreski et al. 2008, Jacimovic et al. 2008). Iron chlorocomplexes were extracted with di-i-propyl ether (DIPE) or i-amyl acetate (lAA). After Fe elimination, the distribution of 35-39 elements in the extraction systems was determined. Twelve to fourteen elements, particularly the lanthanides, could be detected with increased sensitivity, while Sb, Mo, Au, Se and Te were co-extracted with Fe, which prevented the determination of these elements. 

Preferential absorption of OSO4 has been shown [115] to reveal spherulites in semicrystalline PET. Stefan and Williams [116] work on ABS-poly-carbonate blends also showed contrast by selective absorption. The dark SAN polymer, in this latter study, contains the osmium stained rubber particles while the polycarbonate was not stained. Niimoni et al. [117] found that there is often enough phase contrast in stained copolymers which have different degrees of unsaturation or functional groups like -OH, -0-, or as they each vary in reactivity with the stain. A specially constructed pressure bomb was developed by Edwards and Phillips [118] in order to terminate crystallization and fix polymers with OSO4 at elevated pressure. This method has permitted determination of lamellar growth rates and the observation of developments in crystalline morphology. 

The five parts describe discrete units of subject matter, but nevertheless the book does not necessarily have to be read in a linear fashion from beginning to end. The individual chapters have been written so that they constitute self-contained modules, and so one can always be skipped. In this way, we have tried to make the character of the book meet the criteria of a reference work. Different interpretations of a topic by different authors have been accepted, as has some repetition, so as not to disrupt the flow of the writing. Finally, some important areas have been covered by several authors, who have naturally placed more emphasis on certain aspects. This applies, for example, to pH (Uwe D. Neue, Michael McBrien), weighted regression Hans-Joachim Kuss, Stefan Schomer), the selectivity of stationary RP phases Stavros Kromidas, Uwe D. Neue, Melvin R. Euerhy, Cinzia Stella, Lloyd R. Snyder), chemometrics Stavros Kromidas, Melvin R. Euerhy, Cinzia Stella), and LC-MS Friedrich Mandel, Katrin Markus). The reader may benefit from the different descriptions of the topics and from the individual evaluations of the authors. 

Q/A)p is evaluated from the Stefan-Boltzmann radiation heat ilux equation. Even though there are wide variations in the reported values of frost emissivity and absorptivity, the total heat flux is little affected by the emissivity value selected because the magnitude of the resulting heat flux is conveniently small as compared to the convection and mass transfer heat fliixes. 

The separation factor of these organic polymer membranes is typically located in a moderate range, of around 5 and 10, but rarely higher than 20. As a rule of thumb and proven by recent publications, the membrane selectivity can be approximated as the product of the adsorption selectivity and diffusion selectivity [2]. This chapter provides a wealth of information on diffusion inside micro- and mesoporous structures using concepts and ideas that originate from Maxwell and Stefan. A molecular-level understanding of diffusion in a variety of materials such as zeolites, MOFs, covalent organic frameworks (COFs), carbon nanotubes, and cylindrical silica pores is provided with the aid of extensive data sets of molecular... 

An older general review by Stefan et al. [2] considers mathematical modeling for data processing (including a variety of chemometric methods such as linear and nonlinear partial least squares, fuzzy neural networks, and multivariate analysis of variance), designs for electrochemical sensor arrays as well as applications in environmental, food and clinical analysis. Arrays of potentiometric ion-selective electrodes, piezoelectric crystal sensors, and voltammetric biosensors, as well as the electronic nose gas-phase sensor arrays are reviewed. 

The set of two coupled partial differential equations (equation 5.18) subject to the initial and boundary conditions (equations 5.19 and 5.20) were solved using the method of lines [211] to determine the fluxes, as described in ref. [212]. In the calculations presented here we assume that the pure component Maxwell-Stefan diffusivities are identiccd for the isomers, i.e. D iz = D 2z this assumption is a conservative one from the viewpoint of sepeiration of the isomers as we expect the branched isomer to have a lower mobility within the Siliccdite structure. The simulations were carried out with the complete Maxwell-Stefan model for [D], i.e. equation 5.14. Since the interchange coefficient D12 has a value intermediate between Diz and D2Z [213] we must also have D iz = Dzz = D 12. A further point to note is that in the calculation of the fluxes we have made the assumption that the Maxwell-Stefan diffusivities are independent of the loading. Though this assumption is not always true (see refs. [214,215]), the values of the ratio of fluxes, i.e. selectivity for separation, is not expected to be influenced by this assumption. 

With the selection of a reference velocity, the Stefan-Maxwell equations can be inverted to yield flux equations. We choose the reference velocity to be that of the solvent and consider the case of a binary electrolyte, for which flux equations can be obtained for both the cation and anion. Since usually only the cation reacts in lithium batteries, the equations are made simpler later on if we focus ordy on a mass balance for the anion. By electroneutrality, the mass balance for the anion must be identical to that for the cation. The flux equation for the anion obtained from inverting the Stefan-MaxweU equations is... 

The description of the separation of multicomponent mixtures requires a more complex approach, for example by using Maxwell-Stefan methodology. However, the real membrane often assumes a more complex structure, in which, beside the microporous zeolite layer, the mesoporosity of the intra-crystalline-defects and of the underlying support can play an important role, especially when the capillary condensation phenomenon can occur, as in the case of the permeation of vapour. Kondo and Kita (Kondo and Kita, 2010) attempted an interpretation of the dehydration process by including narrow non-zeolitic pores into the support. The water molecules in the feed selectively adsorbed in zeolite pores are then transported to the non-zeolitic pore, where they are released in the permeate side of the membrane. 

Vessman J, Stefan RI, Van Staden JF et al (2001) Selectivity in analytical chemistry. Pure Appl Chem 73 1381-1386... 

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